Conjecture and Question

[Mason Malmuth]

Hi eric:

Great post.

Best wishes,
mason

[Mason Malmuth]

Hi Zoot:

I disagree. To play a successful "big stack game" you need opponents whose stacks are starting to put them in jeapordy (but not yet tiny). After the first hand of the tourney, this won't be the case.

Best wishes,
Mason

[dogsballs]

[ QUOTE ]
Even though chips were issued at a 1chip = $1 scale, they don't pay that way.

[/ QUOTE ]


This is why.


It doesn't need to be big and mathematically funky, with odd proofs and analogies.


edit: make it a SNG. You go all-in with all but one other player and win....you have 9 tenths (or 8 ninths) of the chips but only a max of one half of the prize pool equity (actually a bit less).

Reedit: Doh! one half not one third.

[DonT77]

After pondering this some more, I think the Finance Equation for Future Value is more applicable in a winner-take-all type of format where cEV is closer to $EV at the end of the tournament - because getting all the chips does not get you all of the money in most large MTTs where the winner usually only gets ~25% of the prize pool.

I think the Future Value formula might have some merit when it comes to projecting the size of ones stack say mid-way through a tournament, but once the blinds get bigger and the pots get bigger and variances get larger and the payout get nearer - I think it loses most of its validity.

In other, more simplified words, we can use the FV equation for cEV but not for $EV.


One other factor that has not been mentioned yet is the 'time' factor. In a MTT, it is the person who lasts the longest who wins the most money - and the longer you last the more money you make. By having more chips, you not only have the big stack benefits already mentioned, but you also have more 'time' - time to survive, time to wait for better situations or bigger hands, time to setup plays, time to change gears, etc. Note that in the FV equation the n - factor is the number of periods. In an MTT this could be hands, levels, hours, or whatever - but the more periods you are alive for and the larger your stack and the larger your growth rate - the larger you future stack should be and the more money you should make.


So how does all this relate to Mason's question - I think that by doubling up the first hand you can more than double your chip expectancy for midway through the tournament, but I don't think that it approaches doubling your $ expectancy at the end of a tournament.

It would be interesting if we hand enough hand histories, to figure out at what point a player doubled his initial stack and how that actually relates to his $EV.

[Stickleback]

The great player’s increased expectations implies that he will, over a sufficient sample set of tournaments, increase his chip count faster than an average player. Therefore, during the early and middle stages of a tournament, he is expected to have a larger than average stack. Doubling through an average stack will result in a stack that is still less than double his expected stack at that stage of the tournament.

Steve

[valenzuela]

My post will contain random statements. They might mean abosoluely nothing.

1)lets suppose that everyone has 10k, the blinds are 50k-100k with 10k antes, the pro has an expectation of 10k.
lets suppose that everyone has 10k, the blinds are 500-1000, the pro has an expectation of 13K.

2)lets suppose that everyone has 10k, the blinds are 25-50 the, pro has an expectation of 40K...however the pro will only have 39.96K of expectation if he folds the first hand, after every hand the pro expectation decreases a tiny bit unless he increases his stack.

3)lets suppose the pro can win 50 chips in every 25-50 hand he plays with a stack of 10k. Its obvious that the pro will be able to win >50 chips in every 25-50 hand with a stack of 20k.( unless nobody has more than 10k)

IMO the flaw in everybody who agree with the statement is theyre not taking into account the loss on the pro expectation after every hand that goes by without chip profit.( im talking about early stages )

[Dave D]

I've tried to read everyone's posts, and I'm gonna try to throw in my own thoughts on this.

My thesis here is: After the tournament starts, there's no way to know what your expectation is. I think once you make your judgement at the start of the tourney, that's all you have, and obviously that's shaky in itself, here's why I think this:

1. I look at trying to re-evaluate your expectation as analogous to the comment I occasionally see fish make. You're both all in preflop, you have Ak and he has a pair, you hit your A on the river. The fish says "nice river", or "river saved you". We all know this isn't the case, you had 5 chances to hit and you did.

I think this is the same as the situation we're talking about. Before the tournament starts, you somehow made a judgement as to your expectation, which theoretically should have considered every possible outcome. On avg, you expect to be up x amount. Doubling up in the first hand should have already been considered as one of these. You can't make any sort of new judgements, because you already have. I think you're basically being results oriented when you start trying to re-evaluate your expectation.

So basically what I'm saying is, this specific outcome doesn't matter.

2. I like the Golf analogy. However, I'd like to make a football analogy. Similar, but a little distinct, and a little more extreme, and therefore I think fits better.

Pretty much any football game, the halftime score isn't that important most of the time. That is, if you tell me USC is beating Bama by 7-0 at halftime, you're basically telling me *nothing* about the outcome. I'd say this is probably going to be the case up to around a 17 point difference. Witness UT coming back against LSU this year, and UT has had a horrible season.

So, what I'm saying is, doubling up early on is pretty useless. I mean, it's nice, it feels good, but ultimatly, in the grand scheme of information that you're talking about, it's really not important, at all. Anything could happen, the next hand you could lose with AA against AK AI PF. You could get moved to a table with all pros and be at the ONE table without bad players.

If say in the first 5 hands you have doubled up each time, yeah, then it starts to matter. But until you can really say you have a *dominating* chip stack, I dont think your expectation changes significantly. Having twice everyone else's stack just isn't that big a deal. Things will be evened out in an hour.

3. Furthermore, I think expectation calculations are pretty much useless. As they say in commercials for mutual funds, past performance does not indicate future success. but nevermind that, even if your ROI is a certain number of a lot of tournaments, I just view it as useless to try to calculate expectation. You play the best game you can and hope to do well.

[MLG]

Hi Mason:

[ QUOTE ]
Hi TV:

I don't think so. Using Harrington terminology, there is no question that when your M is 10 you have playing advantages over opponents whose M is 5. But when your M is 80, I don't believe you have any advantages over someone whose M is 40.

Best wishes,
Mason

[/ QUOTE ]

I strenuosly disagree with this. If nothing else having and M of 80 allows you to win twice as many chips as a player who's M is 40. Also, while this might not make itself apparent in any individual hand, the player with an M of 80 will be able to play more speculative hands until the blinds go up or his stack bleeds away than the player with the M of 40 will. So, he in effect has twice as many opporunities to flop a big hand and win a big pot and further grow his stack. Those are the two issues that come to mind immediately but there may be more.

Best wishes,
Mike

[El Diablo]

I just wanna chime in to repeat what has already been said (just because some people are prone to discount posts from "lesser-known" posters). Very nice post.

[AtticusFinch]

[ QUOTE ]
Hi Atticus:

Your example may not be relevant since it effectively ends the tournament. In my question knocking one person out and you having double the chips really has no impact.

best wishes,
mason

[/ QUOTE ]

It says little about your particular problem, that's true. I just use it to illustrate the notion that the relationship between your stack size and your $EV is not a straight linear one, even in a WTA tourney.